I agree with your concern. This is a lightly built pendant, and you're talking about adding a significant amount of weight to it. The pendant's electrical cord (presuming it passed UL testing)* is only made to carry what's part of it now.
The normal way to support a heavy luminaire is to use a chain (as part of the design aesthetic) or thin steel cable (if aiming to conceal) to carry the physical weight. The electrical cord is not load-bearing at all, and simply runs through the chain/alongside the cable. It may be possible to buy lamp cordage with the steel cable integrated. A steel cable can serve as a grounding wire; a chain cannot. Neutral must be an actual wire.
A third way is to use steel tubing and run the cable down the tubing. The tubing size is limited by the minimum size for luminaire wire: 18AWG.
It may also be possible to devise a harness which supports the wine bottle only, e.g. by supporting a ring on the inside of the wine bottle -- and then, thread the luminaire through all that, so the luminaire does not bear any weight.
You can hang up to 4 pounds of weight from any junction box without having to do anything special, and I don't see this exceeding that weight.
As far as undesired lumpy switches on cords, that's irrelevant since you'll have to snip off the plug anyway. A wine bottle neck is too narrow to pass even a NEMA 1 connector through. Installing a replacement plug is Code legal, or you can hardwire straight up into a junction box.
Now there's yet another option to make this work: low voltage lighting. Low voltage devices less than 55 watts are subject to a more relaxed set of rules. This practically requires LED, but LED is very good now.
* Amazon is an "open access platform". Amazon allows third party sellers to sell via their website and use their warehouses, which has become a superhighway for cheap Cheese junk that can't pass our safety laws (e.g. UL listing). Brick-and-mortar retail stores like Target or Lowes generally stock legal products. So does Amazon proper, which you can identify by This item is Sold by and ships from amazon.com in the listing. This product is fine.
UL is one of several Nationally Recognized Testing Laboratories. Also acceptable: CSA, TUV, ETL and a few others. CE is not one.